Prep ingredients. Pull the butter, eggs, and milk out of the fridge at least 1 hour before you bake. (See note)
Prep the pan and oven. Preheat to 360°F (180°C). Generously grease a 10-cup Bundt pan with soft butter, then dust with flour and tap out the excess.
Cream the butter. In the bowl of a stand mixer fitted with the paddle attachment (or a large bowl with a hand mixer), beat the butter on medium until smooth, about 30 seconds.
1 ¼ cups unsalted butter
Add sugar, vanilla, rum, and salt. Beat on medium-high for 2 full minutes until the mixture looks pale and fluffy.
1 ¼ cups granulated sugar, 2 teaspoons vanilla extract, 1 tablespoon dark rum, ½ teaspoon salt
Add eggs one at a time. Crack in 1 egg, beat on medium-high for 30 seconds, then add the next. Repeat until all 5 are in. The batter should look smooth. If it curdles slightly, don't panic; it'll come back together once the flour goes in.
5 large eggs
Combine the dry ingredients. In a separate bowl, whisk the flour and baking powder together.
2 ½ cups all-purpose flour, 4 teaspoons baking powder
Alternate flour and milk. On low speed, add the flour in 3 parts and the milk in 2, starting and ending with flour. The batter will be thick. Do not overmix once the flour is in.
¼ cup milk
Divide the batter. Transfer about 2/3 of the batter (roughly 900 g if you have a scale) into the prepared Bundt pan.
Make the chocolate batter. Sift the cocoa powder into the remaining 1/3 of the batter, add the milk, and mix until smooth and evenly brown.
5 tablespoons Dutch-processed cocoa powder, 2 tablespoons milk
Add and swirl. Dollop the chocolate batter in spoonfuls over the light batter. Take a fork (or a thin knife) and drag it through in 4–5 figure eights. Gently tap the pan several times on the countertop to dislodge any air bubbles and smooth the top of the batter with a spatula.
Bake. Place on the middle rack and bake for 50 minutes. Start checking after 45 minutes. The cake is done when the top is deeply golden and a skewer inserted in the thickest part comes out with a few dry crumbs (not wet batter). If it's not done, give it another 5–10 minutes. If the top is browning too fast, tent loosely with foil.
Cool. Let the cake rest in the pan for 10 minutes. Run a thin knife around the outer edge and the center tube, set a cooling rack on top of the pan, and flip in one confident motion. Let it cool completely, at least 1 hour, before glazing.
Make the glaze. Chop the chocolate into small, even pieces. Combine with the coconut oil in a microwave-safe bowl. Microwave in 30-second bursts, stirring between each, until just melted and smooth. Usually 60–90 seconds total. Don't overheat, or the chocolate will seize. Let it sit for 2–3 minutes so it thickens slightly. You can also melt it in a double boiler on the stove over low heat.
6 oz semi-sweet chocolate, 2 tablespoons coconut oil
Glaze the cake. Brush or spoon the glaze over the cooled cake, letting it drip down the ridges. Let the chocolate set at room temperature for about 30 minutes before slicing.